Champlain College Physics 203-NYC

Simple Harmonic Motion

List of problems in OpenStax University Physics, Volume 1, chapter 15:22, 23, 24, 25, 28, 29, 30. 38, 41, 56

1 Additional Problems

1. The phase of an oscillating particle can be visualized as a point moving counterclockwisearound a unit circle at constant speed. For each of the phase constants given below:

• Assume a particle’s position given by A cos(ωt+ φ0)

• Show with a dot on the unit circle the phase of the particle’s starting position.

• Sketch two cycles of the particle’s x-vs-t graph.

(a) φ0 = 0 rad

(b) φ0 = π2rad

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Champlain College Physics 203-NYC

(c) φ0 = πrad

(d) φ0 = −π2rad

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Champlain College Physics 203-NYC

2. The graph below represents a particle in simple harmonic motion.

(a) using x(t) = A cos(ωt+ φ0), what is the phase constant φ0?

(b) What is the phase of the function at each of the three numbered points on thegraph?

(c) Place dots in the unit circle above to show the position of these three phases. Labeleach dot with the appropriate number.

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Champlain College Physics 203-NYC

3. For each graph below, determine A, ω, and φ0.

(a)

(b)

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Champlain College Physics 203-NYC

(c)

4. a 507 g mass oscillates with an amplitude of 10 cm on a spring whose spring constantis 20 N/m. At t = 0 s the mass is 5.0 cm to the right of the equilibrium position andmoving to the right. Determine:

(a) The period (T ).

(b) The angular frequency (ω).

(c) The phase constant (φ0).

(d) The initial velocity.

(e) The maximum speed.

(f) The position at t = 1.3 s.

(g) The velocity at t = 1.3 s.

(h) Identify which graph on the following page best represents the position vs time ofthe oscillating mass

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Champlain College Physics 203-NYC

A B

C D

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